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For many machine learning algorithms, their success heavily depends on data representation. In this paper, we present an ${\ell }_{2,1}$ -norm constrained canonical correlation analysis (CCA) model, that is, $ {L}_{{2,1}}$ -CCA, toward discovering compact and discriminative representation for the data associated with multiple views. To well exploit the complementary and coherent information across multiple views, the ${\ell }_{{2,1}}$ -norm is employed to constrain the canonical loadings and measure the canonical correlation loss term simultaneously. It enables, on the one hand, the canonical loadings to be with the capacity of variable selection for facilitating the interpretability of the learned canonical variables, and on the other hand, the learned canonical common representation keeps highly consistent with the most canonical variables from each view of the data. Meanwhile, the proposed ${L}_{{2,1}}$ -CCA can also be provided with the desired insensitivity to noise (outliers) to some degree. To solve the optimization problem, we develop an efficient alternating optimization algorithm and give its convergence analysis both theoretically and experimentally. Considerable experiment results on several real-world datasets have demonstrated that ${L}_{{2,1}}$ -CCA can achieve competitive or better performance in comparison with some representative approaches for multiview representation learning.

This paper investigates simultaneous wireless information and power transfer (SWIPT) in energy harvesting (EH) relay systems. Unlike the existing SWIPT schemes requiring the instantaneous channel state information (CSI) for coherent information delivery, we propose a noncoherent SWIPT framework for decode-and-forward (DF) relay systems bypassing the need for the instantaneous CSI and consequently saving energy in the network. The proposed SWIPT framework embraces both the power-splitting noncoherent DF (PS-NcDF) and time-switching noncoherent DF (TS-NcDF) in a unified form, and supports arbitrary $M$ -ary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK). The exact (noncoherent) maximum-likelihood detectors (MLDs) for PS-NcDF and TS-NcDF are derived in a unified form, which involves integral evaluations yet serves as the optimum performance benchmark for noncoherent SWIPT. To reduce the computational cost of the exact MLDs, we also propose closed-form approximate MLDs achieving near-optimum performance, thus serving as a practical solution for noncoherent SWIPT. Numerical results demonstrate a performance tradeoff between the first and second hops through the adjustment of time switching or power splitting parameters, whose optimal values minimizing the symbol-error rate (SER) are strictly between 0 and 1. We demonstrate that $M$ -FSK results in a significant energy saving over $M$ -DPSK for $M\ge 8$ ; thus $M$ -FSK may be more suitable for EH relay systems.

Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In the current paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper. Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much like Devetak's technique for demonstrating the achievability of the coherent information rate for quantum data transmission. Our scheme achieves the symmetric coherent information rate for quantum channels that are degradable with a classical environment. This condition on the environment may seem restrictive, but we show that many quantum channels satisfy this criterion, including amplitude damping channels, photon-detected jump channels, dephasing channels, erasure channels, and cloning channels. Our quantum polar coding scheme has the desirable properties of being channel-adapted and symmetric capacity-achieving along with having an efficient encoder, but we have not demonstrated that the decoding is efficient. Also, the scheme may require entanglement assistance, but we show that the rate of entanglement consumption vanishes in the limit of large blocklength if the channel is degradable with classical environment., 12 pages, 1 figure; v2: IEEE format, minor changes including new figure; v3: minor changes, accepted for publication in IEEE Transactions on Information Theory

The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a recovery map that exactly reverses the effects of the quantum channel on both states. In this paper, we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case, we reproduce recent lower bounds on the conditional mutual information, such as the one proved by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm., National Science Foundation (U.S.) (CF-1111382), National Science Foundation (U.S.) (CF-1452616), United States. Army Research Office (W911NF-12-1- 0486)

Optimal utilization of complex synthetic aperture radar imagery for coherent change detection (CCD) is achieved by maximizing the amount of information extracted from the coherent correlation of images. Conventional techniques cannot fully exploit the coherent information due to limited application of few products or indicators, e.g., correlation factor and phase maps. Also, considering the lack of a systematic formulation of change observables and their nature, unsupervised change detection or classification is not feasible. To address this, an analytic framework is established by taking advantage of the analogy to partially polarized electromagnetic fields to introduce vectors and observables that can establish a complete change space. Decomposition of the coherent correlation or change characteristics into this basis set can provide a better understanding of the associated change phenomenology.

Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement manipulation of an asymptotically large number of copies of the states. In this paper, different asymptotic measures of entanglement assigned to arbitrary sequences of bipartite pure states are shown to coincide only when the sequence is information stable, in terms of the quantum spectral information rates of the sequence of subsystem states. Additional bounds on the optimal rates of entanglement manipulation protocols in quantum information are also presented, including bounds given by generalizations of the coherent information and the relative entropy of entanglement., Comment: 7 pages, requires IEEEtran.cls

Quantum distortion operator is introduced based on canonical operators. As the lower bound of quantum information rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. The entanglement information rate-distortion function is calculated for one-mode Gaussian source, it is achieved by a nontrivial unitary transformation. The rate distortion is achievable at zero distortion point. In contrast to the distortion defined via fidelity, our definition of the distortion makes it possible to calculate the entanglement information rate-distortion function for Gaussian source.

A relationship between information theory and estimation theory was recently shown for the Gaussian channel, relating the derivative of mutual information with the minimum mean-square error. This paper generalizes the link between information theory and estimation theory to arbitrary channels, giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs. We illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an unrestricted classical side channel, we find the exact quantum rate-distortion function for a source of isotropic qubits. An upper bound we believe to be exact is found in the case of biased sources. We establish that in this scenario optimal rate-distortion codes produce no entropy exchange with the environment of any individual qubit.

We prove a data processing inequality for quantum communication channels, which states that processing a received quantum state may never increase the mutual information between input and output states., 8 pages

Information theorists frequently use the ergodic theorem; likewise entropy concepts are often used in information theory. Recently, the two subjects have become partially intertwined as deeper results from each discipline find use in the other. A brief history of this interaction is presented in this paper, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.

It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.

Two classes of coherent radar types are analyzed to ascertain whether any significant advantages exist for a given system. The classes compared are those coherent radars which transmit a phasecoherent pulse-to-pulse RF carrier as opposed to those which transmit randomly phased RF carriers but store the coherent information at the radar for Doppler extraction. Rigorous new analytical development is avoided in favor of examination of the considerable existing literature, examination of practical limitations, and synthesis of generic solutions from key concepts. Examination is made of coherent radar classes from the viewpoints of reconnaissance ance and intelligence measurement, new radar design and devlopment, and electronic countermeasures vulnerability. The conclusion that the classes of coherent radars examined have a priori and a posteriori equivalent performance has significant implications not published in any reference source.

Given a finite number of quantum states with {\em a priori} probabilities, the positive operator-valued measure that maximizes the Shannon mutual information is investigated. The group covariant case is examined in detail.

A quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed. The mutual information of quantum communication theory is defined by using the compound state, and its fundamental properties are studied.

This paper discusses the architecture of a metasystem, which can be used to generate intelligent information systems for different domains of discourse. It points out the kinds of knowledge accepted by the system, and the way the knowledge is used to do nontrivial problem solving. The organization of the system makes it possible for it to function in the context of a large and expanding data base. The metasystem provides a basis for the definition of the concept of machine understanding in terms of the models that the machine can build in a domain, and the way it can use the models.